TS EAMCET · Maths · Definite Integration
\(\int_0^{\pi / 2} \frac{d x}{1+\tan ^3 x}\) is equal to :
- A \(\pi\)
- B \(\frac{\pi}{2}\)
- C \(\frac{\pi}{4}\)
- D \(\frac{3 \pi}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi}{4}\)
Step-by-step Solution
Detailed explanation
\(I=\int_0^{\pi / 2} \frac{d x}{1+\tan ^3 x}\) \(I=\int_0^{\pi / 2} \frac{\cos ^3 x}{\sin ^3 x+\cos ^3 x} d x\) ...(i) \(I=\int_0^{\pi / 2} \frac{\cos ^3\left(\frac{\pi}{2}-x\right)}{\sin ^3\left(\frac{\pi}{2}-x\right)+\cos ^3\left(\frac{\pi}{2}-x\right)} d x\)…
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